Material Modeling in Finite Element Analysis

Zhaochun Yang

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781000691054
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Finite element analysis has been widely applied in mechanical, civil, and biomedical designs. This book aims to provide the readers comprehensive views of various material models with practical examples, which would help readers understand various materials, and build appropriate material models in the finite element analysis.

This book is composed of four main parts: 1) metals, 2) polymers, 3) soils, and 4) modern materials. Each part starts with the structure and function of different materials and then follows the corresponding material models such as BISO, MISO, Chaboche model in metals, Arruda-Boyce model, Mooney-Rivlin model, Ogden model in polymers, Mohr-Coulomb model, Cam Clay model and Jointed Rock model in geomechanics, composites and shape memory alloys in modern materials. The final section presents some specific problems, such as metal forming process, combustion chamber, Mullins effect of rubber tire, breast shape after breast surgery, viscoelasticity of liver soft tissues, tunnel excavation, slope stability, orthodontic wire, and piezoelectric microaccelerometer. All modeling files are provided in the appendixes of the book.

This book would be helpful for graduate students and researchers in the mechanical, civil, and biomedical fields who conduct finite element analysis. The book provides all readers with comprehensive understanding of modeling various materials.

1

Introduction

We live in a modern world of buildings, cars, airplanes, and medical advances, including coronary angioplasty. Buildings require structural analysis from civil engineers, while the manufacture of cars and airplanes depends upon strong mechanical design. Biomedical engineering plays a significant role in coronary surgeries. All these fields demand an understanding of the stress state of the structures. With the development of computer technology, finite element analysis has been widely used in these fields. Specifically, since the 1970s, many commercial finite element software companies have evolved: ANSYS, ABAQUS, COMSOL, ADINA, LS-DYNA, and MARC. Among these, ANSYS emerges as the leader.

One of the key processes in finite element analysis is to build material models. The structural analysis of a building is associated with soils, the manufacture of a car involves metals, the airplane has many components made of composites to ensure both high strength and low weight, and the stent in the coronary angioplasty is made of shape memory alloys. When we create finite element models to conduct stress analysis for their designs, we must adopt a variety of material models corresponding to different materials, because under the same geometry and loadings and boundary conditions, different materials may have unique behaviors. For example, it is hard to pull a steel rod, but the same force can easily deform a rubber rod. If we pull the metal rod to plasticity, the plastic strains remain after the force is gone. However, when the metal rod is made of shape memory alloys, the remaining transformation strains can be removed with the rise of temperature. Unlike these materials, soil has little resistance to tension. The purpose of this book is to acknowledge that different materials have unique features and to present readers with comprehensive views of various material models. By providing practical examples, the book will enable readers to better understand the material models, how to select appropriate material models, and how to define the correct solution set in the finite element analysis of complicated engineering problems. As discussed above, ANSYS is the leading software in the field of finite element analysis. Thus, the examples in the book are provided in the form of ANSYS input files, which makes it convenient for readers to learn and practice these examples.

The book is composed of four main parts. After the introductory chapter, the first part focuses on metals and alloys. Chapter 2 introduces the structure of alloys and mechanical features. Some plastic models such as the bilinear isotropic hardening model, the multilinear isotropic hardening model, the Voce law nonlinear isotropic hardening model, and the Chaboche model, along with examples showing how to determine material parameters from the experimental data, are presented in Chapter 3. Chapter 4 discusses the application of plastic models for simulation of the forming process, including one example of a sheet that is deformed between two dies. Ratcheting is one unique feature of plastic metals under cyclic loading. It is reproduced on a notched rod with the Chaboche kinematic hardening material model under cyclic loading in Chapter 5. As the material properties of metals are temperature-dependent, Chapter 6 examines the influence of temperature on a combustion chamber. The last chapter in Part I develops the creep subroutine and applies it to simulate the creep behavior of the metal under pretension.

Part II discusses polymers. After Chapter 8 depicts the structure and material properties of polymers, Chapter 9 presents some hyperelastic material models, including two examples: the large deformation of a rubber rod and the deformation of a breast after breast surgery. The viscoelasticity of polymers and its application for liver soft tissues are discussed in Chapter 10. The stress responses of elastomers always experience softening during the first few loading cycles. That is regarded as a damage accumulation in the material, which refers to the Mullins effect of elastomers. Chapter 11 focuses on this and includes an example of a rubber tire. Userhyper is available in ANSYS for the customers to create their own hyperelastic models. Chapter 12 presents one example of Userhyper to reproduce the Gent model.

Soils are the topic of Part III. Chapter 13 introduces the structure and various classifications of soils. Four major material models of soils – the Cam Clay model, Drucker–Prager model, Mohr–Coulomb model, and jointed rock model – are discussed in Chapters 14 to 17, respectively. These chapters also cover some practical problems: a tower on the ground, soil–arch interaction, the stability of a slope, and a tunnel excavation. Since soils are composed of rocks, water, and air, Chapter 18 focuses on the consolidation of soils and its application for simulation of consolidation of rocks with three wells.

Part IV highlights modern materials. One widely used modern material is composite, which was developed in the 1950s due to airplane design needing high strength and low weight. Structure and material properties of composites are presented in the first part of Chapter 19, followed by an application on flight-qualification testing and crack growth in single-leg bending problem.

Chapter 20 examines functionally graded materials and their simulation in ANSYS using TBFIELD technology.

The unique features of shape memory alloys (SMAs), superelasticity and shape memory effect, are discussed in Chapter 21. The chapter includes two examples to demonstrate SMAs’ applications: (1) orthodontic wire using the superelasticity feature and (2) a vacuum-tight shape memory flange using shape memory effect.

Chapter 22 reviews the structure and mechanical behavior of piezoelectric materials. This is followed by the simulation of a thin film piezoelectric microaccelerometer using the piezoelectric material model in ANSYS.

Nanoscale materials refer to a group of substances with at least one dimension less than approximately 100 nm, which attract more and more interest. The first part of Chapter 23 introduces the nanoscale materials; in the second part, Young’s modulus of nano Fe particles is determined from the experimental data of a ball made of Fe particles using the optimization algorithm in ANSYS.

Chapter 24 reviews the features of metals/alloys, polymers, soils, and modern materials, and discusses the relation between material properties and the structures as well as the relation between the temperature and the structure. It also examines solution control for various materials, including anisotropic materials with symmetrical conditions.

Part I

Metal

Metal plays a dominant role in modern industry, especially in the manufacturing of cars, airplanes, and ships. Its mechanical design requires a clear understanding of its stress-and-strain state. Therefore, Part I focuses on many metal material models implemented in ANSYS.

Chapter 2 introduces the structure and material properties of metal. Some plastic models, including the material parameters determined from the experimental data, are discussed in Chapter 3. Chapters 4 and 5 simulate metal forming and ratcheting, respectively. The influence of temperature on the material properties is analyzed in Chapter 6, and creep is simulated by both ANSYS and user subroutine in Chapter 7.

2

Structure and Material Properties of Metal

The material properties of metal are closely linked with the structure of metal. Thus, this chapter first presents the structure of metal and then gives the material properties of metal.

2.1 Structure of Metal

A metal is a material in which the atoms are joined together by metallic bonds...